The investigation of tissue magnetic susceptibility and the resultant magnetic field offers a new avenue for quantitative tissue characterisation by MRI. One crucial step in mining the phase and field data for relevant tissue information is the correction of externally induced field shifts. This article outlines a multistep approach comprising several methodologies for background field removal. The virtues of B0 long-range variation detection and compensation of more localised external disturbances are unified in a sequential filter chain. The algorithm is tested by means of a numerical Monte Carlo simulation model and applied to in vivo measurements at 3T and 9.4T as well as to a fixed brain tissue measurement at 9.4T. Further, a comparison to conventional filter types has been undertaken.